No one in their right mind would suggest a sport involving dozens of horses, people and dogs trampling miles of countryside as a sensible culling method. The reason these people support fox-hunting is, as they freely admit, that they enjoy it. And it is precisely this that is wrong with it.
This is not about foxes, it is about us. As the planet's supposedly superior species it behoves us to sanctify all other life forms. Where environmental considerations necessitate the taking of life, we should take no pleasure in it, but perform it as an unwelcome duty, as humanely as possible, respectfully and with regret.